The singer, whose real name was Michael Lee Aday, has sold millions of albums worldwide, with the Bat Out Of Hell trilogy among his most popular musical offerings.
His hit single I’d Do Anything For Love (But I Won’t Do That) reached number one in 28 countries and earned him a Grammy award.
The statement said: “Our hearts are broken to announce that the incomparable Meat Loaf passed away tonight with his wife Deborah by his side. Daughters Pearl and Amanda and close friends have been with him throughout the last 24 hours.
“His amazing career spanned six decades that saw him sell over 100 million albums worldwide and star in over 65 movies, including Fight Club, Focus, Rocky Horror Picture Show and Wayne’s World.
“Bat Out of Hell remains one of the top 10 selling albums of all time.
“We know how much he meant to so many of you and we truly appreciate all of the love and support as we move through this time of grief in losing such an inspiring artist and beautiful man.
“We thank you for your understanding of our need for privacy at this time.
“From his heart to your souls…don’t ever stop rocking!”
The rocker also played the role of Eddie in the 1975 musical film The Rocky Horror Picture Show, and in 2016 was honoured with the Hero Award at the annual Q Awards music ceremony, which he dedicated to everyday heroes and called on people to “bring love back into this world”.
Bat Out Of Hell was also adapted as a stage musical, which has been performed in Edinburgh and was written by long-time collaborator Jim Steinman and featured some of the musician’s best-loved hits.
Meat Loaf had spoken openly about health issues that had plagued him, notably asthma, which caused him to collapse on stage during a concert in Pittsburgh in 2011, and in 2003 he collapsed at Wembley Arena in London and was admitted to hospital.
Following an on-stage collapse in Canada in 2016, a statement issued at the time said it had been down to “severe dehydration”.
Stephen Fry has written a tribute to singer Meat Loaf, who has died at the age of 74.
The actor said in a tweet: “I hope paradise is as you remember it from the dashboard light, Meat Loaf.
“Had a fun time performing a sketch with him on Saturday Live way back in the last century.”
BBC Radio 2 DJ Jo Whiley paid tribute to Meat Loaf, describing his voice as “extraordinary”.
She wrote in a tweet: “God I loved Bat Out of Hell. Soundtrack to my youth. Sad news RIP Meatloaf.
“Extraordinary voice. Phenomenonal (sic) character.”